FUNDAMENTAL OF DIGITAL ELECTRONICS�(CODE: 3310702)

BINARY SYSTEMS

BRIEF INTRODUCTION OF ALL UNITS�

POINTS TO BE COVERED

• Introduction of Digital Computers and Digital Systems
• Binary numbers
• Base Conversion
• BINARY
• DECIMAL
• HEX
• OCTAL
• Complements ,R’s Complement ,2’ and 10’s Complement ,R-1)’s Complement
• 1’s and 9’s Complement
• Binary Codes
• Decimal Codes
• Error Detection codes
• Reflected Code

INTRODUCTION OF DIGITAL COMPUTERS AND DIGITAL SYSTEMS�

• Digital systems are used in communication, business transactions, traffic control, spacecraft guidance, medical treatment, weather monitoring, the Internet, and many other commercial, industrial, and scientific enterprises
• The most striking property of the digital computer is its generality. It can follow a sequence of instructions, called a program, that operates on given data.
• The user can specify and change the program or the data according to the specific need. Because of this flexibility, general‐purpose digital computers can perform a variety of information‐processing tasks that range over a wide spectrum of applications..
• One characteristic of digital systems is their ability to represent and manipulate dis-crete elements of information.
• Discrete elements of information are represented in a digital system by physical quantities called signals.
• The signals in most present‐day electronic digital systems use just two discrete values and are therefore said to be binary. A binary digit, called a bit, has two values: 0 and 1. Discrete elements of information are represented with groups of bits called binary codes.
• A digital system is an interconnection of digital modules. To understand the operation of each digital module, it is necessary to have a basic knowledge of digital circuits and their logical function.

BINARY NUMBERS

• A decimal number such as 7,392 represents a quantity equal to 7 thousands, plus 3 hundreds, plus 9 tens, plus 2 units.

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• The decimal number system is said to be of base, or radix, 10 because it uses 10 digits and the coefficients are multiplied by powers of 10. The binary system is a different number system.
• The coefficients of the binary number system have only two possible values: 0 and 1. Each coefficient aj is multiplied by a power of the radix, e.g., 2j, and the results are added to obtain the decimal equivalent of the number.

NUMBER BASE CONVERSION

• Representations of a number in a different radix are said to be equivalent if they have the same decimal representation. For example, (0011) 8 and (1001) 2 are equivalent—both have decimal value 9.
• The conversion of a number in base r to decimal is done by expanding the number in a power series and adding all the terms.
• he conversion of a decimal integer to a number in base r is done by dividing the number and all successive quotients by r and accumulating the remainders.

COMPLEMENTS OF NUMBERS

• Complements are used in digital computers to simplify the subtraction operation and for logical manipulation.
• Simplifying operations leads to simpler, less expensive circuits to implement the operations.
• There are two types of complements for each base‐r system: the radix complement and the diminished radix complement. The first is referred to as the r’s complement and the second as the (r-1)’s complement.

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